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Pré-Publication, Document De Travail Année : 2021

Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation

Résumé

We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tends to points, to get solutions to the KdV equation given in terms of Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, Fredholm determinants and wronskians. This gives the bridge between the algebro-geometric approach and the Darboux dressing method.
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Dates et versions

hal-03327882 , version 1 (27-08-2021)

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  • HAL Id : hal-03327882 , version 1

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Pierre Gaillard. Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation. 2021. ⟨hal-03327882⟩
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